LMFDB - Embedded newform 6010.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.35701 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.35701 q^{6} +1.93749 q^{7} -1.00000 q^{8} +8.26955 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.35701 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.35701 q^{6} +1.93749 q^{7} -1.00000 q^{8} +8.26955 q^{9} +1.00000 q^{10} +4.37555 q^{11} -3.35701 q^{12} +6.33095 q^{13} -1.93749 q^{14} +3.35701 q^{15} +1.00000 q^{16} -6.50823 q^{17} -8.26955 q^{18} +6.98680 q^{19} -1.00000 q^{20} -6.50420 q^{21} -4.37555 q^{22} -0.991065 q^{23} +3.35701 q^{24} +1.00000 q^{25} -6.33095 q^{26} -17.6900 q^{27} +1.93749 q^{28} +4.13656 q^{29} -3.35701 q^{30} -2.57782 q^{31} -1.00000 q^{32} -14.6888 q^{33} +6.50823 q^{34} -1.93749 q^{35} +8.26955 q^{36} -3.55077 q^{37} -6.98680 q^{38} -21.2531 q^{39} +1.00000 q^{40} -5.58686 q^{41} +6.50420 q^{42} +3.16004 q^{43} +4.37555 q^{44} -8.26955 q^{45} +0.991065 q^{46} -3.58195 q^{47} -3.35701 q^{48} -3.24612 q^{49} -1.00000 q^{50} +21.8482 q^{51} +6.33095 q^{52} -7.99139 q^{53} +17.6900 q^{54} -4.37555 q^{55} -1.93749 q^{56} -23.4548 q^{57} -4.13656 q^{58} -10.7856 q^{59} +3.35701 q^{60} +0.782070 q^{61} +2.57782 q^{62} +16.0222 q^{63} +1.00000 q^{64} -6.33095 q^{65} +14.6888 q^{66} -9.90828 q^{67} -6.50823 q^{68} +3.32702 q^{69} +1.93749 q^{70} +0.364597 q^{71} -8.26955 q^{72} -10.5095 q^{73} +3.55077 q^{74} -3.35701 q^{75} +6.98680 q^{76} +8.47761 q^{77} +21.2531 q^{78} -7.28525 q^{79} -1.00000 q^{80} +34.5768 q^{81} +5.58686 q^{82} -5.69015 q^{83} -6.50420 q^{84} +6.50823 q^{85} -3.16004 q^{86} -13.8865 q^{87} -4.37555 q^{88} -13.2147 q^{89} +8.26955 q^{90} +12.2662 q^{91} -0.991065 q^{92} +8.65378 q^{93} +3.58195 q^{94} -6.98680 q^{95} +3.35701 q^{96} +15.7976 q^{97} +3.24612 q^{98} +36.1839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.35701	−1.93817	−0.969087	−	0.246720i	$-0.920647\pi$
$3$	−3.35701	−1.93817	−0.969087	+	0.246720i	$0.920647\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.35701	1.37050
$7$	1.93749	0.732304	0.366152	−	0.930555i	$-0.380675\pi$
$7$	1.93749	0.732304	0.366152	+	0.930555i	$0.380675\pi$
$8$	−1.00000	−0.353553
$9$	8.26955	2.75652
$10$	1.00000	0.316228
$11$	4.37555	1.31928	0.659640	−	0.751582i	$-0.270709\pi$
$11$	4.37555	1.31928	0.659640	+	0.751582i	$0.270709\pi$
$12$	−3.35701	−0.969087
$13$	6.33095	1.75589	0.877945	−	0.478761i	$-0.158914\pi$
$13$	6.33095	1.75589	0.877945	+	0.478761i	$0.158914\pi$
$14$	−1.93749	−0.517817
$15$	3.35701	0.866778
$16$	1.00000	0.250000
$17$	−6.50823	−1.57848	−0.789239	−	0.614086i	$-0.789525\pi$
$17$	−6.50823	−1.57848	−0.789239	+	0.614086i	$0.789525\pi$
$18$	−8.26955	−1.94915
$19$	6.98680	1.60288	0.801441	−	0.598074i	$-0.204067\pi$
$19$	6.98680	1.60288	0.801441	+	0.598074i	$0.204067\pi$
$20$	−1.00000	−0.223607
$21$	−6.50420	−1.41933
$22$	−4.37555	−0.932871
$23$	−0.991065	−0.206651	−0.103326	−	0.994648i	$-0.532948\pi$
$23$	−0.991065	−0.206651	−0.103326	+	0.994648i	$0.532948\pi$
$24$	3.35701	0.685248
$25$	1.00000	0.200000
$26$	−6.33095	−1.24160
$27$	−17.6900	−3.40443
$28$	1.93749	0.366152
$29$	4.13656	0.768141	0.384070	−	0.923304i	$-0.374522\pi$
$29$	4.13656	0.768141	0.384070	+	0.923304i	$0.374522\pi$
$30$	−3.35701	−0.612904
$31$	−2.57782	−0.462990	−0.231495	−	0.972836i	$-0.574362\pi$
$31$	−2.57782	−0.462990	−0.231495	+	0.972836i	$0.574362\pi$
$32$	−1.00000	−0.176777
$33$	−14.6888	−2.55699
$34$	6.50823	1.11615
$35$	−1.93749	−0.327496
$36$	8.26955	1.37826
$37$	−3.55077	−0.583743	−0.291872	−	0.956457i	$-0.594278\pi$
$37$	−3.55077	−0.583743	−0.291872	+	0.956457i	$0.594278\pi$
$38$	−6.98680	−1.13341
$39$	−21.2531	−3.40322
$40$	1.00000	0.158114
$41$	−5.58686	−0.872522	−0.436261	−	0.899820i	$-0.643697\pi$
$41$	−5.58686	−0.872522	−0.436261	+	0.899820i	$0.643697\pi$
$42$	6.50420	1.00362
$43$	3.16004	0.481902	0.240951	−	0.970537i	$-0.422541\pi$
$43$	3.16004	0.481902	0.240951	+	0.970537i	$0.422541\pi$
$44$	4.37555	0.659640
$45$	−8.26955	−1.23275
$46$	0.991065	0.146125
$47$	−3.58195	−0.522482	−0.261241	−	0.965274i	$-0.584132\pi$
$47$	−3.58195	−0.522482	−0.261241	+	0.965274i	$0.584132\pi$
$48$	−3.35701	−0.484543
$49$	−3.24612	−0.463731
$50$	−1.00000	−0.141421
$51$	21.8482	3.05936
$52$	6.33095	0.877945
$53$	−7.99139	−1.09770	−0.548851	−	0.835920i	$-0.684935\pi$
$53$	−7.99139	−1.09770	−0.548851	+	0.835920i	$0.684935\pi$
$54$	17.6900	2.40730
$55$	−4.37555	−0.590000
$56$	−1.93749	−0.258909
$57$	−23.4548	−3.10666
$58$	−4.13656	−0.543157
$59$	−10.7856	−1.40417	−0.702085	−	0.712093i	$-0.747747\pi$
$59$	−10.7856	−1.40417	−0.702085	+	0.712093i	$0.747747\pi$
$60$	3.35701	0.433389
$61$	0.782070	0.100134	0.0500669	−	0.998746i	$-0.484057\pi$
$61$	0.782070	0.100134	0.0500669	+	0.998746i	$0.484057\pi$
$62$	2.57782	0.327383
$63$	16.0222	2.01861
$64$	1.00000	0.125000
$65$	−6.33095	−0.785258
$66$	14.6888	1.80807
$67$	−9.90828	−1.21049	−0.605245	−	0.796040i	$-0.706925\pi$
$67$	−9.90828	−1.21049	−0.605245	+	0.796040i	$0.706925\pi$
$68$	−6.50823	−0.789239
$69$	3.32702	0.400526
$70$	1.93749	0.231575
$71$	0.364597	0.0432697	0.0216349	−	0.999766i	$-0.493113\pi$
$71$	0.364597	0.0432697	0.0216349	+	0.999766i	$0.493113\pi$
$72$	−8.26955	−0.974576
$73$	−10.5095	−1.23005	−0.615024	−	0.788508i	$-0.710854\pi$
$73$	−10.5095	−1.23005	−0.615024	+	0.788508i	$0.710854\pi$
$74$	3.55077	0.412769
$75$	−3.35701	−0.387635
$76$	6.98680	0.801441
$77$	8.47761	0.966113
$78$	21.2531	2.40644
$79$	−7.28525	−0.819655	−0.409828	−	0.912163i	$-0.634411\pi$
$79$	−7.28525	−0.819655	−0.409828	+	0.912163i	$0.634411\pi$
$80$	−1.00000	−0.111803
$81$	34.5768	3.84187
$82$	5.58686	0.616966
$83$	−5.69015	−0.624575	−0.312287	−	0.949988i	$-0.601095\pi$
$83$	−5.69015	−0.624575	−0.312287	+	0.949988i	$0.601095\pi$
$84$	−6.50420	−0.709666
$85$	6.50823	0.705917
$86$	−3.16004	−0.340756
$87$	−13.8865	−1.48879
$88$	−4.37555	−0.466436
$89$	−13.2147	−1.40076	−0.700380	−	0.713770i	$-0.746986\pi$
$89$	−13.2147	−1.40076	−0.700380	+	0.713770i	$0.746986\pi$
$90$	8.26955	0.871687
$91$	12.2662	1.28585
$92$	−0.991065	−0.103326
$93$	8.65378	0.897355
$94$	3.58195	0.369450
$95$	−6.98680	−0.716830
$96$	3.35701	0.342624
$97$	15.7976	1.60400	0.802002	−	0.597321i	$-0.203768\pi$
$97$	15.7976	1.60400	0.802002	+	0.597321i	$0.203768\pi$
$98$	3.24612	0.327907
$99$	36.1839	3.63662
$100$	1.00000	0.100000
$101$	−18.5608	−1.84687	−0.923433	−	0.383760i	$-0.874629\pi$
$101$	−18.5608	−1.84687	−0.923433	+	0.383760i	$0.874629\pi$
$102$	−21.8482	−2.16330
$103$	4.08304	0.402314	0.201157	−	0.979559i	$-0.435530\pi$
$103$	4.08304	0.402314	0.201157	+	0.979559i	$0.435530\pi$
$104$	−6.33095	−0.620801
$105$	6.50420	0.634744
$106$	7.99139	0.776193
$107$	−4.59412	−0.444130	−0.222065	−	0.975032i	$-0.571280\pi$
$107$	−4.59412	−0.444130	−0.222065	+	0.975032i	$0.571280\pi$
$108$	−17.6900	−1.70222
$109$	3.99175	0.382341	0.191170	−	0.981557i	$-0.438772\pi$
$109$	3.99175	0.382341	0.191170	+	0.981557i	$0.438772\pi$
$110$	4.37555	0.417193
$111$	11.9200	1.13140
$112$	1.93749	0.183076
$113$	9.61616	0.904612	0.452306	−	0.891863i	$-0.350601\pi$
$113$	9.61616	0.904612	0.452306	+	0.891863i	$0.350601\pi$
$114$	23.4548	2.19674
$115$	0.991065	0.0924173
$116$	4.13656	0.384070
$117$	52.3541	4.84014
$118$	10.7856	0.992898
$119$	−12.6097	−1.15593
$120$	−3.35701	−0.306452
$121$	8.14548	0.740498
$122$	−0.782070	−0.0708052
$123$	18.7552	1.69110
$124$	−2.57782	−0.231495
$125$	−1.00000	−0.0894427
$126$	−16.0222	−1.42737
$127$	−5.09293	−0.451925	−0.225962	−	0.974136i	$-0.572553\pi$
$127$	−5.09293	−0.451925	−0.225962	+	0.974136i	$0.572553\pi$
$128$	−1.00000	−0.0883883
$129$	−10.6083	−0.934009
$130$	6.33095	0.555261
$131$	3.38566	0.295807	0.147903	−	0.989002i	$-0.452748\pi$
$131$	3.38566	0.295807	0.147903	+	0.989002i	$0.452748\pi$
$132$	−14.6888	−1.27850
$133$	13.5369	1.17380
$134$	9.90828	0.855945
$135$	17.6900	1.52251
$136$	6.50823	0.558076
$137$	4.60060	0.393056	0.196528	−	0.980498i	$-0.437033\pi$
$137$	4.60060	0.393056	0.196528	+	0.980498i	$0.437033\pi$
$138$	−3.32702	−0.283215
$139$	−14.7081	−1.24752	−0.623761	−	0.781615i	$-0.714396\pi$
$139$	−14.7081	−1.24752	−0.623761	+	0.781615i	$0.714396\pi$
$140$	−1.93749	−0.163748
$141$	12.0247	1.01266
$142$	−0.364597	−0.0305963
$143$	27.7014	2.31651
$144$	8.26955	0.689129
$145$	−4.13656	−0.343523
$146$	10.5095	0.869776
$147$	10.8973	0.898791
$148$	−3.55077	−0.291872
$149$	9.74616	0.798436	0.399218	−	0.916856i	$-0.369282\pi$
$149$	9.74616	0.798436	0.399218	+	0.916856i	$0.369282\pi$
$150$	3.35701	0.274099
$151$	−19.8464	−1.61508	−0.807538	−	0.589816i	$-0.799200\pi$
$151$	−19.8464	−1.61508	−0.807538	+	0.589816i	$0.799200\pi$
$152$	−6.98680	−0.566704
$153$	−53.8201	−4.35110
$154$	−8.47761	−0.683145
$155$	2.57782	0.207055
$156$	−21.2531	−1.70161
$157$	4.10713	0.327785	0.163892	−	0.986478i	$-0.447595\pi$
$157$	4.10713	0.327785	0.163892	+	0.986478i	$0.447595\pi$
$158$	7.28525	0.579584
$159$	26.8272	2.12754
$160$	1.00000	0.0790569
$161$	−1.92018	−0.151332
$162$	−34.5768	−2.71661
$163$	−21.0807	−1.65117	−0.825586	−	0.564277i	$-0.809155\pi$
$163$	−21.0807	−1.65117	−0.825586	+	0.564277i	$0.809155\pi$
$164$	−5.58686	−0.436261
$165$	14.6888	1.14352
$166$	5.69015	0.441641
$167$	−8.40106	−0.650094	−0.325047	−	0.945698i	$-0.605380\pi$
$167$	−8.40106	−0.650094	−0.325047	+	0.945698i	$0.605380\pi$
$168$	6.50420	0.501810
$169$	27.0810	2.08315
$170$	−6.50823	−0.499159
$171$	57.7777	4.41837
$172$	3.16004	0.240951
$173$	−11.3864	−0.865693	−0.432847	−	0.901468i	$-0.642491\pi$
$173$	−11.3864	−0.865693	−0.432847	+	0.901468i	$0.642491\pi$
$174$	13.8865	1.05273
$175$	1.93749	0.146461
$176$	4.37555	0.329820
$177$	36.2075	2.72153
$178$	13.2147	0.990487
$179$	−4.64204	−0.346963	−0.173481	−	0.984837i	$-0.555502\pi$
$179$	−4.64204	−0.346963	−0.173481	+	0.984837i	$0.555502\pi$
$180$	−8.26955	−0.616376
$181$	−18.9122	−1.40573	−0.702866	−	0.711322i	$-0.748097\pi$
$181$	−18.9122	−1.40573	−0.702866	+	0.711322i	$0.748097\pi$
$182$	−12.2662	−0.909230
$183$	−2.62542	−0.194077
$184$	0.991065	0.0730623
$185$	3.55077	0.261058
$186$	−8.65378	−0.634526
$187$	−28.4771	−2.08245
$188$	−3.58195	−0.261241
$189$	−34.2742	−2.49308
$190$	6.98680	0.506876
$191$	−8.91538	−0.645094	−0.322547	−	0.946553i	$-0.604539\pi$
$191$	−8.91538	−0.645094	−0.322547	+	0.946553i	$0.604539\pi$
$192$	−3.35701	−0.242272
$193$	15.8993	1.14446	0.572229	−	0.820094i	$-0.306079\pi$
$193$	15.8993	1.14446	0.572229	+	0.820094i	$0.306079\pi$
$194$	−15.7976	−1.13420
$195$	21.2531	1.52197
$196$	−3.24612	−0.231866
$197$	25.0301	1.78332	0.891661	−	0.452704i	$-0.149541\pi$
$197$	25.0301	1.78332	0.891661	+	0.452704i	$0.149541\pi$
$198$	−36.1839	−2.57148
$199$	−6.29894	−0.446520	−0.223260	−	0.974759i	$-0.571670\pi$
$199$	−6.29894	−0.446520	−0.223260	+	0.974759i	$0.571670\pi$
$200$	−1.00000	−0.0707107
$201$	33.2622	2.34614
$202$	18.5608	1.30593
$203$	8.01457	0.562512
$204$	21.8482	1.52968
$205$	5.58686	0.390204
$206$	−4.08304	−0.284479
$207$	−8.19566	−0.569638
$208$	6.33095	0.438973
$209$	30.5711	2.11465
$210$	−6.50420	−0.448832
$211$	−13.2392	−0.911424	−0.455712	−	0.890127i	$-0.650615\pi$
$211$	−13.2392	−0.911424	−0.455712	+	0.890127i	$0.650615\pi$
$212$	−7.99139	−0.548851
$213$	−1.22396	−0.0838643
$214$	4.59412	0.314047
$215$	−3.16004	−0.215513
$216$	17.6900	1.20365
$217$	−4.99451	−0.339049
$218$	−3.99175	−0.270356
$219$	35.2807	2.38405
$220$	−4.37555	−0.295000
$221$	−41.2033	−2.77163
$222$	−11.9200	−0.800018
$223$	−26.0814	−1.74654	−0.873270	−	0.487236i	$-0.838005\pi$
$223$	−26.0814	−1.74654	−0.873270	+	0.487236i	$0.838005\pi$
$224$	−1.93749	−0.129454
$225$	8.26955	0.551303
$226$	−9.61616	−0.639658
$227$	−20.9408	−1.38989	−0.694946	−	0.719062i	$-0.744572\pi$
$227$	−20.9408	−1.38989	−0.694946	+	0.719062i	$0.744572\pi$
$228$	−23.4548	−1.55333
$229$	16.7372	1.10603	0.553014	−	0.833172i	$-0.313478\pi$
$229$	16.7372	1.10603	0.553014	+	0.833172i	$0.313478\pi$
$230$	−0.991065	−0.0653489
$231$	−28.4595	−1.87250
$232$	−4.13656	−0.271579
$233$	−12.8242	−0.840144	−0.420072	−	0.907491i	$-0.637995\pi$
$233$	−12.8242	−0.840144	−0.420072	+	0.907491i	$0.637995\pi$
$234$	−52.3541	−3.42250
$235$	3.58195	0.233661
$236$	−10.7856	−0.702085
$237$	24.4567	1.58863
$238$	12.6097	0.817363
$239$	−5.38960	−0.348624	−0.174312	−	0.984690i	$-0.555770\pi$
$239$	−5.38960	−0.348624	−0.174312	+	0.984690i	$0.555770\pi$
$240$	3.35701	0.216694
$241$	4.37644	0.281912	0.140956	−	0.990016i	$-0.454982\pi$
$241$	4.37644	0.281912	0.140956	+	0.990016i	$0.454982\pi$
$242$	−8.14548	−0.523611
$243$	−63.0049	−4.04177
$244$	0.782070	0.0500669
$245$	3.24612	0.207387
$246$	−18.7552	−1.19579
$247$	44.2331	2.81448
$248$	2.57782	0.163692
$249$	19.1019	1.21053
$250$	1.00000	0.0632456
$251$	5.71873	0.360963	0.180482	−	0.983578i	$-0.442234\pi$
$251$	5.71873	0.360963	0.180482	+	0.983578i	$0.442234\pi$
$252$	16.0222	1.00930
$253$	−4.33646	−0.272631
$254$	5.09293	0.319559
$255$	−21.8482	−1.36819
$256$	1.00000	0.0625000
$257$	−19.9392	−1.24377	−0.621887	−	0.783107i	$-0.713634\pi$
$257$	−19.9392	−1.24377	−0.621887	+	0.783107i	$0.713634\pi$
$258$	10.6083	0.660444
$259$	−6.87960	−0.427477
$260$	−6.33095	−0.392629
$261$	34.2075	2.11739
$262$	−3.38566	−0.209167
$263$	−7.40015	−0.456313	−0.228156	−	0.973625i	$-0.573270\pi$
$263$	−7.40015	−0.456313	−0.228156	+	0.973625i	$0.573270\pi$
$264$	14.6888	0.904033
$265$	7.99139	0.490907
$266$	−13.5369	−0.829999
$267$	44.3621	2.71492
$268$	−9.90828	−0.605245
$269$	31.2662	1.90634	0.953168	−	0.302442i	$-0.0978019\pi$
$269$	31.2662	1.90634	0.953168	+	0.302442i	$0.0978019\pi$
$270$	−17.6900	−1.07658
$271$	24.7045	1.50069	0.750346	−	0.661046i	$-0.229887\pi$
$271$	24.7045	1.50069	0.750346	+	0.661046i	$0.229887\pi$
$272$	−6.50823	−0.394620
$273$	−41.1777	−2.49219
$274$	−4.60060	−0.277932
$275$	4.37555	0.263856
$276$	3.32702	0.200263
$277$	−15.8261	−0.950901	−0.475451	−	0.879742i	$-0.657715\pi$
$277$	−15.8261	−0.950901	−0.475451	+	0.879742i	$0.657715\pi$
$278$	14.7081	0.882131
$279$	−21.3174	−1.27624
$280$	1.93749	0.115787
$281$	−7.85620	−0.468662	−0.234331	−	0.972157i	$-0.575290\pi$
$281$	−7.85620	−0.468662	−0.234331	+	0.972157i	$0.575290\pi$
$282$	−12.0247	−0.716059
$283$	−22.5915	−1.34292	−0.671462	−	0.741039i	$-0.734333\pi$
$283$	−22.5915	−1.34292	−0.671462	+	0.741039i	$0.734333\pi$
$284$	0.364597	0.0216349
$285$	23.4548	1.38934
$286$	−27.7014	−1.63802
$287$	−10.8245	−0.638951
$288$	−8.26955	−0.487288
$289$	25.3571	1.49159
$290$	4.13656	0.242907
$291$	−53.0328	−3.10884
$292$	−10.5095	−0.615024
$293$	−17.7509	−1.03702	−0.518510	−	0.855072i	$-0.673513\pi$
$293$	−17.7509	−1.03702	−0.518510	+	0.855072i	$0.673513\pi$
$294$	−10.8973	−0.635541
$295$	10.7856	0.627964
$296$	3.55077	0.206384
$297$	−77.4034	−4.49140
$298$	−9.74616	−0.564580
$299$	−6.27439	−0.362857
$300$	−3.35701	−0.193817
$301$	6.12256	0.352898
$302$	19.8464	1.14203
$303$	62.3088	3.57955
$304$	6.98680	0.400720
$305$	−0.782070	−0.0447812
$306$	53.8201	3.07669
$307$	11.3444	0.647461	0.323730	−	0.946149i	$-0.395063\pi$
$307$	11.3444	0.647461	0.323730	+	0.946149i	$0.395063\pi$
$308$	8.47761	0.483057
$309$	−13.7068	−0.779754
$310$	−2.57782	−0.146410
$311$	−11.3977	−0.646305	−0.323152	−	0.946347i	$-0.604743\pi$
$311$	−11.3977	−0.646305	−0.323152	+	0.946347i	$0.604743\pi$
$312$	21.2531	1.20322
$313$	17.7951	1.00584	0.502920	−	0.864333i	$-0.332259\pi$
$313$	17.7951	1.00584	0.502920	+	0.864333i	$0.332259\pi$
$314$	−4.10713	−0.231779
$315$	−16.0222	−0.902749
$316$	−7.28525	−0.409828
$317$	−1.64646	−0.0924744	−0.0462372	−	0.998930i	$-0.514723\pi$
$317$	−1.64646	−0.0924744	−0.0462372	+	0.998930i	$0.514723\pi$
$318$	−26.8272	−1.50440
$319$	18.0998	1.01339
$320$	−1.00000	−0.0559017
$321$	15.4225	0.860801
$322$	1.92018	0.107008
$323$	−45.4717	−2.53011
$324$	34.5768	1.92093
$325$	6.33095	0.351178
$326$	21.0807	1.16755
$327$	−13.4004	−0.741042
$328$	5.58686	0.308483
$329$	−6.94001	−0.382615
$330$	−14.6888	−0.808592
$331$	−9.39163	−0.516211	−0.258105	−	0.966117i	$-0.583098\pi$
$331$	−9.39163	−0.516211	−0.258105	+	0.966117i	$0.583098\pi$
$332$	−5.69015	−0.312287
$333$	−29.3633	−1.60910
$334$	8.40106	0.459686
$335$	9.90828	0.541347
$336$	−6.50420	−0.354833
$337$	20.6389	1.12427	0.562136	−	0.827045i	$-0.309980\pi$
$337$	20.6389	1.12427	0.562136	+	0.827045i	$0.309980\pi$
$338$	−27.0810	−1.47301
$339$	−32.2816	−1.75330
$340$	6.50823	0.352958
$341$	−11.2794	−0.610813
$342$	−57.7777	−3.12426
$343$	−19.8518	−1.07190
$344$	−3.16004	−0.170378
$345$	−3.32702	−0.179121
$346$	11.3864	0.612137
$347$	−1.46009	−0.0783818	−0.0391909	−	0.999232i	$-0.512478\pi$
$347$	−1.46009	−0.0783818	−0.0391909	+	0.999232i	$0.512478\pi$
$348$	−13.8865	−0.744395
$349$	−27.0392	−1.44738	−0.723688	−	0.690127i	$-0.757554\pi$
$349$	−27.0392	−1.44738	−0.723688	+	0.690127i	$0.757554\pi$
$350$	−1.93749	−0.103563
$351$	−111.994	−5.97781
$352$	−4.37555	−0.233218
$353$	−19.1727	−1.02046	−0.510229	−	0.860038i	$-0.670439\pi$
$353$	−19.1727	−1.02046	−0.510229	+	0.860038i	$0.670439\pi$
$354$	−36.2075	−1.92441
$355$	−0.364597	−0.0193508
$356$	−13.2147	−0.700380
$357$	42.3308	2.24038
$358$	4.64204	0.245340
$359$	−17.1786	−0.906650	−0.453325	−	0.891345i	$-0.649762\pi$
$359$	−17.1786	−0.906650	−0.453325	+	0.891345i	$0.649762\pi$
$360$	8.26955	0.435843
$361$	29.8154	1.56923
$362$	18.9122	0.994003
$363$	−27.3445	−1.43521
$364$	12.2662	0.642923
$365$	10.5095	0.550095
$366$	2.62542	0.137233
$367$	34.5954	1.80586	0.902932	−	0.429783i	$-0.141410\pi$
$367$	34.5954	1.80586	0.902932	+	0.429783i	$0.141410\pi$
$368$	−0.991065	−0.0516628
$369$	−46.2008	−2.40512
$370$	−3.55077	−0.184596
$371$	−15.4833	−0.803852
$372$	8.65378	0.448677
$373$	−25.5431	−1.32257	−0.661285	−	0.750135i	$-0.729989\pi$
$373$	−25.5431	−1.32257	−0.661285	+	0.750135i	$0.729989\pi$
$374$	28.4771	1.47252
$375$	3.35701	0.173356
$376$	3.58195	0.184725
$377$	26.1884	1.34877
$378$	34.2742	1.76287
$379$	7.87360	0.404440	0.202220	−	0.979340i	$-0.435184\pi$
$379$	7.87360	0.404440	0.202220	+	0.979340i	$0.435184\pi$
$380$	−6.98680	−0.358415
$381$	17.0970	0.875908
$382$	8.91538	0.456151
$383$	10.7313	0.548343	0.274171	−	0.961681i	$-0.411596\pi$
$383$	10.7313	0.548343	0.274171	+	0.961681i	$0.411596\pi$
$384$	3.35701	0.171312
$385$	−8.47761	−0.432059
$386$	−15.8993	−0.809254
$387$	26.1321	1.32837
$388$	15.7976	0.802002
$389$	−28.7592	−1.45815	−0.729074	−	0.684435i	$-0.760049\pi$
$389$	−28.7592	−1.45815	−0.729074	+	0.684435i	$0.760049\pi$
$390$	−21.2531	−1.07619
$391$	6.45008	0.326195
$392$	3.24612	0.163954
$393$	−11.3657	−0.573324
$394$	−25.0301	−1.26100
$395$	7.28525	0.366561
$396$	36.1839	1.81831
$397$	−2.91628	−0.146364	−0.0731820	−	0.997319i	$-0.523315\pi$
$397$	−2.91628	−0.146364	−0.0731820	+	0.997319i	$0.523315\pi$
$398$	6.29894	0.315738
$399$	−45.4435	−2.27502
$400$	1.00000	0.0500000
$401$	37.0237	1.84887	0.924437	−	0.381336i	$-0.124536\pi$
$401$	37.0237	1.84887	0.924437	+	0.381336i	$0.124536\pi$
$402$	−33.2622	−1.65897
$403$	−16.3200	−0.812959
$404$	−18.5608	−0.923433
$405$	−34.5768	−1.71813
$406$	−8.01457	−0.397756
$407$	−15.5366	−0.770121
$408$	−21.8482	−1.08165
$409$	−11.4833	−0.567812	−0.283906	−	0.958852i	$-0.591630\pi$
$409$	−11.4833	−0.567812	−0.283906	+	0.958852i	$0.591630\pi$
$410$	−5.58686	−0.275916
$411$	−15.4443	−0.761810
$412$	4.08304	0.201157
$413$	−20.8971	−1.02828
$414$	8.19566	0.402795
$415$	5.69015	0.279318
$416$	−6.33095	−0.310400
$417$	49.3752	2.41791
$418$	−30.5711	−1.49528
$419$	36.9382	1.80455	0.902274	−	0.431163i	$-0.141897\pi$
$419$	36.9382	1.80455	0.902274	+	0.431163i	$0.141897\pi$
$420$	6.50420	0.317372
$421$	−21.8683	−1.06580	−0.532898	−	0.846180i	$-0.678897\pi$
$421$	−21.8683	−1.06580	−0.532898	+	0.846180i	$0.678897\pi$
$422$	13.2392	0.644474
$423$	−29.6211	−1.44023
$424$	7.99139	0.388096
$425$	−6.50823	−0.315696
$426$	1.22396	0.0593010
$427$	1.51525	0.0733283
$428$	−4.59412	−0.222065
$429$	−92.9941	−4.48980
$430$	3.16004	0.152391
$431$	9.10953	0.438790	0.219395	−	0.975636i	$-0.429592\pi$
$431$	9.10953	0.438790	0.219395	+	0.975636i	$0.429592\pi$
$432$	−17.6900	−0.851108
$433$	−14.1771	−0.681307	−0.340653	−	0.940189i	$-0.610648\pi$
$433$	−14.1771	−0.681307	−0.340653	+	0.940189i	$0.610648\pi$
$434$	4.99451	0.239744
$435$	13.8865	0.665807
$436$	3.99175	0.191170
$437$	−6.92437	−0.331238
$438$	−35.2807	−1.68578
$439$	0.0571635	0.00272827	0.00136413	−	0.999999i	$-0.499566\pi$
$439$	0.0571635	0.00272827	0.00136413	+	0.999999i	$0.499566\pi$
$440$	4.37555	0.208596
$441$	−26.8439	−1.27828
$442$	41.2033	1.95984
$443$	25.6264	1.21755	0.608774	−	0.793344i	$-0.291662\pi$
$443$	25.6264	1.21755	0.608774	+	0.793344i	$0.291662\pi$
$444$	11.9200	0.565698
$445$	13.2147	0.626439
$446$	26.0814	1.23499
$447$	−32.7180	−1.54751
$448$	1.93749	0.0915380
$449$	26.2962	1.24100	0.620498	−	0.784208i	$-0.286931\pi$
$449$	26.2962	1.24100	0.620498	+	0.784208i	$0.286931\pi$
$450$	−8.26955	−0.389830
$451$	−24.4456	−1.15110
$452$	9.61616	0.452306
$453$	66.6246	3.13030
$454$	20.9408	0.982802
$455$	−12.2662	−0.575047
$456$	23.4548	1.09837
$457$	−6.37167	−0.298054	−0.149027	−	0.988833i	$-0.547614\pi$
$457$	−6.37167	−0.298054	−0.149027	+	0.988833i	$0.547614\pi$
$458$	−16.7372	−0.782079
$459$	115.130	5.37382
$460$	0.991065	0.0462087
$461$	15.9140	0.741190	0.370595	−	0.928794i	$-0.379154\pi$
$461$	15.9140	0.741190	0.370595	+	0.928794i	$0.379154\pi$
$462$	28.4595	1.32405
$463$	1.66602	0.0774266	0.0387133	−	0.999250i	$-0.487674\pi$
$463$	1.66602	0.0774266	0.0387133	+	0.999250i	$0.487674\pi$
$464$	4.13656	0.192035
$465$	−8.65378	−0.401309
$466$	12.8242	0.594072
$467$	−31.2528	−1.44620	−0.723102	−	0.690741i	$-0.757285\pi$
$467$	−31.2528	−1.44620	−0.723102	+	0.690741i	$0.757285\pi$
$468$	52.3541	2.42007
$469$	−19.1972	−0.886446
$470$	−3.58195	−0.165223
$471$	−13.7877	−0.635304
$472$	10.7856	0.496449
$473$	13.8269	0.635763
$474$	−24.4567	−1.12333
$475$	6.98680	0.320576
$476$	−12.6097	−0.577963
$477$	−66.0852	−3.02583
$478$	5.38960	0.246514
$479$	12.6868	0.579675	0.289837	−	0.957076i	$-0.406399\pi$
$479$	12.6868	0.579675	0.289837	+	0.957076i	$0.406399\pi$
$480$	−3.35701	−0.153226
$481$	−22.4798	−1.02499
$482$	−4.37644	−0.199342
$483$	6.44608	0.293307
$484$	8.14548	0.370249
$485$	−15.7976	−0.717333
$486$	63.0049	2.85796
$487$	3.69894	0.167615	0.0838076	−	0.996482i	$-0.473292\pi$
$487$	3.69894	0.167615	0.0838076	+	0.996482i	$0.473292\pi$
$488$	−0.782070	−0.0354026
$489$	70.7684	3.20026
$490$	−3.24612	−0.146645
$491$	29.6502	1.33810	0.669048	−	0.743220i	$-0.266702\pi$
$491$	29.6502	1.33810	0.669048	+	0.743220i	$0.266702\pi$
$492$	18.7552	0.845549
$493$	−26.9217	−1.21249
$494$	−44.2331	−1.99014
$495$	−36.1839	−1.62634
$496$	−2.57782	−0.115747
$497$	0.706405	0.0316866
$498$	−19.1019	−0.855977
$499$	−24.9312	−1.11607	−0.558036	−	0.829816i	$-0.688445\pi$
$499$	−24.9312	−1.11607	−0.558036	+	0.829816i	$0.688445\pi$
$500$	−1.00000	−0.0447214
$501$	28.2025	1.25999
$502$	−5.71873	−0.255239
$503$	35.5308	1.58424	0.792119	−	0.610366i	$-0.208978\pi$
$503$	35.5308	1.58424	0.792119	+	0.610366i	$0.208978\pi$
$504$	−16.0222	−0.713685
$505$	18.5608	0.825944
$506$	4.33646	0.192779
$507$	−90.9112	−4.03751
$508$	−5.09293	−0.225962
$509$	5.58801	0.247684	0.123842	−	0.992302i	$-0.460478\pi$
$509$	5.58801	0.247684	0.123842	+	0.992302i	$0.460478\pi$
$510$	21.8482	0.967456
$511$	−20.3622	−0.900769
$512$	−1.00000	−0.0441942
$513$	−123.596	−5.45690
$514$	19.9392	0.879481
$515$	−4.08304	−0.179920
$516$	−10.6083	−0.467004
$517$	−15.6730	−0.689299
$518$	6.87960	0.302272
$519$	38.2244	1.67786
$520$	6.33095	0.277631
$521$	−18.3688	−0.804753	−0.402376	−	0.915474i	$-0.631816\pi$
$521$	−18.3688	−0.804753	−0.402376	+	0.915474i	$0.631816\pi$
$522$	−34.2075	−1.49722
$523$	15.4323	0.674808	0.337404	−	0.941360i	$-0.390451\pi$
$523$	15.4323	0.674808	0.337404	+	0.941360i	$0.390451\pi$
$524$	3.38566	0.147903
$525$	−6.50420	−0.283866
$526$	7.40015	0.322662
$527$	16.7770	0.730819
$528$	−14.6888	−0.639248
$529$	−22.0178	−0.957295
$530$	−7.99139	−0.347124
$531$	−89.1924	−3.87062
$532$	13.5369	0.586898
$533$	−35.3702	−1.53205
$534$	−44.3621	−1.91974
$535$	4.59412	0.198621
$536$	9.90828	0.427973
$537$	15.5834	0.672474
$538$	−31.2662	−1.34798
$539$	−14.2036	−0.611791
$540$	17.6900	0.761254
$541$	−4.58658	−0.197192	−0.0985962	−	0.995128i	$-0.531435\pi$
$541$	−4.58658	−0.197192	−0.0985962	+	0.995128i	$0.531435\pi$
$542$	−24.7045	−1.06115
$543$	63.4885	2.72455
$544$	6.50823	0.279038
$545$	−3.99175	−0.170988
$546$	41.1777	1.76224
$547$	21.7728	0.930936	0.465468	−	0.885065i	$-0.345886\pi$
$547$	21.7728	0.930936	0.465468	+	0.885065i	$0.345886\pi$
$548$	4.60060	0.196528
$549$	6.46736	0.276020
$550$	−4.37555	−0.186574
$551$	28.9013	1.23124
$552$	−3.32702	−0.141607
$553$	−14.1151	−0.600237
$554$	15.8261	0.672389
$555$	−11.9200	−0.505976
$556$	−14.7081	−0.623761
$557$	−14.1536	−0.599707	−0.299854	−	0.953985i	$-0.596938\pi$
$557$	−14.1536	−0.599707	−0.299854	+	0.953985i	$0.596938\pi$
$558$	21.3174	0.902437
$559$	20.0061	0.846166
$560$	−1.93749	−0.0818741
$561$	95.5981	4.03616
$562$	7.85620	0.331394
$563$	−34.6640	−1.46091	−0.730457	−	0.682959i	$-0.760693\pi$
$563$	−34.6640	−1.46091	−0.730457	+	0.682959i	$0.760693\pi$
$564$	12.0247	0.506330
$565$	−9.61616	−0.404555
$566$	22.5915	0.949590
$567$	66.9923	2.81341
$568$	−0.364597	−0.0152982
$569$	9.10585	0.381737	0.190868	−	0.981616i	$-0.438870\pi$
$569$	9.10585	0.381737	0.190868	+	0.981616i	$0.438870\pi$
$570$	−23.4548	−0.982413
$571$	−4.34558	−0.181857	−0.0909285	−	0.995857i	$-0.528983\pi$
$571$	−4.34558	−0.181857	−0.0909285	+	0.995857i	$0.528983\pi$
$572$	27.7014	1.15825
$573$	29.9291	1.25030
$574$	10.8245	0.451807
$575$	−0.991065	−0.0413303
$576$	8.26955	0.344565
$577$	9.08447	0.378191	0.189096	−	0.981959i	$-0.439444\pi$
$577$	9.08447	0.378191	0.189096	+	0.981959i	$0.439444\pi$
$578$	−25.3571	−1.05472
$579$	−53.3742	−2.21816
$580$	−4.13656	−0.171761
$581$	−11.0246	−0.457378
$582$	53.0328	2.19828
$583$	−34.9668	−1.44818
$584$	10.5095	0.434888
$585$	−52.3541	−2.16458
$586$	17.7509	0.733283
$587$	41.0777	1.69546	0.847729	−	0.530430i	$-0.177970\pi$
$587$	41.0777	1.69546	0.847729	+	0.530430i	$0.177970\pi$
$588$	10.8973	0.449396
$589$	−18.0107	−0.742118
$590$	−10.7856	−0.444038
$591$	−84.0265	−3.45639
$592$	−3.55077	−0.145936
$593$	35.2754	1.44859	0.724293	−	0.689493i	$-0.242166\pi$
$593$	35.2754	1.44859	0.724293	+	0.689493i	$0.242166\pi$
$594$	77.4034	3.17590
$595$	12.6097	0.516946
$596$	9.74616	0.399218
$597$	21.1456	0.865434
$598$	6.27439	0.256579
$599$	44.1675	1.80464	0.902318	−	0.431072i	$-0.141864\pi$
$599$	44.1675	1.80464	0.902318	+	0.431072i	$0.141864\pi$
$600$	3.35701	0.137050
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−6.12256	−0.249537
$603$	−81.9370	−3.33673
$604$	−19.8464	−0.807538
$605$	−8.14548	−0.331161
$606$	−62.3088	−2.53112
$607$	−43.4593	−1.76396	−0.881980	−	0.471287i	$-0.843789\pi$
$607$	−43.4593	−1.76396	−0.881980	+	0.471287i	$0.843789\pi$
$608$	−6.98680	−0.283352
$609$	−26.9050	−1.09025
$610$	0.782070	0.0316651
$611$	−22.6772	−0.917421
$612$	−53.8201	−2.17555
$613$	35.7009	1.44194	0.720972	−	0.692964i	$-0.243696\pi$
$613$	35.7009	1.44194	0.720972	+	0.692964i	$0.243696\pi$
$614$	−11.3444	−0.457824
$615$	−18.7552	−0.756282
$616$	−8.47761	−0.341573
$617$	21.4887	0.865103	0.432552	−	0.901609i	$-0.357613\pi$
$617$	21.4887	0.865103	0.432552	+	0.901609i	$0.357613\pi$
$618$	13.7068	0.551370
$619$	−24.7827	−0.996101	−0.498051	−	0.867148i	$-0.665951\pi$
$619$	−24.7827	−0.996101	−0.498051	+	0.867148i	$0.665951\pi$
$620$	2.57782	0.103528
$621$	17.5319	0.703531
$622$	11.3977	0.457006
$623$	−25.6035	−1.02578
$624$	−21.2531	−0.850805
$625$	1.00000	0.0400000
$626$	−17.7951	−0.711237
$627$	−102.628	−4.09856
$628$	4.10713	0.163892
$629$	23.1092	0.921426
$630$	16.0222	0.638340
$631$	−10.1327	−0.403375	−0.201687	−	0.979450i	$-0.564642\pi$
$631$	−10.1327	−0.403375	−0.201687	+	0.979450i	$0.564642\pi$
$632$	7.28525	0.289792
$633$	44.4442	1.76650
$634$	1.64646	0.0653893
$635$	5.09293	0.202107
$636$	26.8272	1.06377
$637$	−20.5510	−0.814261
$638$	−18.0998	−0.716576
$639$	3.01506	0.119274
$640$	1.00000	0.0395285
$641$	10.5241	0.415677	0.207839	−	0.978163i	$-0.433357\pi$
$641$	10.5241	0.415677	0.207839	+	0.978163i	$0.433357\pi$
$642$	−15.4225	−0.608678
$643$	−15.0903	−0.595102	−0.297551	−	0.954706i	$-0.596170\pi$
$643$	−15.0903	−0.595102	−0.297551	+	0.954706i	$0.596170\pi$
$644$	−1.92018	−0.0756658
$645$	10.6083	0.417701
$646$	45.4717	1.78906
$647$	−27.7047	−1.08918	−0.544592	−	0.838701i	$-0.683316\pi$
$647$	−27.7047	−1.08918	−0.544592	+	0.838701i	$0.683316\pi$
$648$	−34.5768	−1.35830
$649$	−47.1931	−1.85249
$650$	−6.33095	−0.248320
$651$	16.7666	0.657136
$652$	−21.0807	−0.825586
$653$	−6.31111	−0.246973	−0.123486	−	0.992346i	$-0.539408\pi$
$653$	−6.31111	−0.246973	−0.123486	+	0.992346i	$0.539408\pi$
$654$	13.4004	0.523996
$655$	−3.38566	−0.132289
$656$	−5.58686	−0.218130
$657$	−86.9092	−3.39065
$658$	6.94001	0.270550
$659$	−11.9602	−0.465902	−0.232951	−	0.972488i	$-0.574838\pi$
$659$	−11.9602	−0.465902	−0.232951	+	0.972488i	$0.574838\pi$
$660$	14.6888	0.571761
$661$	−20.2280	−0.786778	−0.393389	−	0.919372i	$-0.628698\pi$
$661$	−20.2280	−0.786778	−0.393389	+	0.919372i	$0.628698\pi$
$662$	9.39163	0.365016
$663$	138.320	5.37191
$664$	5.69015	0.220821
$665$	−13.5369	−0.524938
$666$	29.3633	1.13780
$667$	−4.09960	−0.158737
$668$	−8.40106	−0.325047
$669$	87.5557	3.38510
$670$	−9.90828	−0.382790
$671$	3.42199	0.132104
$672$	6.50420	0.250905
$673$	−10.1824	−0.392504	−0.196252	−	0.980554i	$-0.562877\pi$
$673$	−10.1824	−0.392504	−0.196252	+	0.980554i	$0.562877\pi$
$674$	−20.6389	−0.794981
$675$	−17.6900	−0.680887
$676$	27.0810	1.04158
$677$	42.2506	1.62382	0.811912	−	0.583780i	$-0.198427\pi$
$677$	42.2506	1.62382	0.811912	+	0.583780i	$0.198427\pi$
$678$	32.2816	1.23977
$679$	30.6078	1.17462
$680$	−6.50823	−0.249579
$681$	70.2987	2.69385
$682$	11.2794	0.431910
$683$	−29.8417	−1.14186	−0.570931	−	0.820998i	$-0.693418\pi$
$683$	−29.8417	−1.14186	−0.570931	+	0.820998i	$0.693418\pi$
$684$	57.7777	2.20918
$685$	−4.60060	−0.175780
$686$	19.8518	0.757945
$687$	−56.1871	−2.14367
$688$	3.16004	0.120475
$689$	−50.5931	−1.92744
$690$	3.32702	0.126658
$691$	−8.38529	−0.318991	−0.159496	−	0.987199i	$-0.550987\pi$
$691$	−8.38529	−0.318991	−0.159496	+	0.987199i	$0.550987\pi$
$692$	−11.3864	−0.432847
$693$	70.1060	2.66311
$694$	1.46009	0.0554243
$695$	14.7081	0.557909
$696$	13.8865	0.526367
$697$	36.3606	1.37726
$698$	27.0392	1.02345
$699$	43.0512	1.62834
$700$	1.93749	0.0732304
$701$	32.1371	1.21380	0.606901	−	0.794778i	$-0.292413\pi$
$701$	32.1371	1.21380	0.606901	+	0.794778i	$0.292413\pi$
$702$	111.994	4.22695
$703$	−24.8085	−0.935671
$704$	4.37555	0.164910
$705$	−12.0247	−0.452875
$706$	19.1727	0.721573
$707$	−35.9614	−1.35247
$708$	36.2075	1.36076
$709$	−36.4452	−1.36873	−0.684364	−	0.729140i	$-0.739920\pi$
$709$	−36.4452	−1.36873	−0.684364	+	0.729140i	$0.739920\pi$
$710$	0.364597	0.0136831
$711$	−60.2458	−2.25939
$712$	13.2147	0.495243
$713$	2.55479	0.0956775
$714$	−42.3308	−1.58419
$715$	−27.7014	−1.03597
$716$	−4.64204	−0.173481
$717$	18.0930	0.675694
$718$	17.1786	0.641098
$719$	−49.4805	−1.84531	−0.922656	−	0.385623i	$-0.873986\pi$
$719$	−49.4805	−1.84531	−0.922656	+	0.385623i	$0.873986\pi$
$720$	−8.26955	−0.308188
$721$	7.91087	0.294616
$722$	−29.8154	−1.10961
$723$	−14.6918	−0.546394
$724$	−18.9122	−0.702866
$725$	4.13656	0.153628
$726$	27.3445	1.01485
$727$	36.6655	1.35985	0.679924	−	0.733283i	$-0.262013\pi$
$727$	36.6655	1.35985	0.679924	+	0.733283i	$0.262013\pi$
$728$	−12.2662	−0.454615
$729$	107.778	3.99178
$730$	−10.5095	−0.388976
$731$	−20.5663	−0.760671
$732$	−2.62542	−0.0970383
$733$	32.9284	1.21624	0.608119	−	0.793846i	$-0.291924\pi$
$733$	32.9284	1.21624	0.608119	+	0.793846i	$0.291924\pi$
$734$	−34.5954	−1.27694
$735$	−10.8973	−0.401952
$736$	0.991065	0.0365312
$737$	−43.3542	−1.59697
$738$	46.2008	1.70068
$739$	20.4411	0.751940	0.375970	−	0.926632i	$-0.377310\pi$
$739$	20.4411	0.751940	0.375970	+	0.926632i	$0.377310\pi$
$740$	3.55077	0.130529
$741$	−148.491	−5.45496
$742$	15.4833	0.568409
$743$	−24.7877	−0.909372	−0.454686	−	0.890652i	$-0.650249\pi$
$743$	−24.7877	−0.909372	−0.454686	+	0.890652i	$0.650249\pi$
$744$	−8.65378	−0.317263
$745$	−9.74616	−0.357071
$746$	25.5431	0.935198
$747$	−47.0549	−1.72165
$748$	−28.4771	−1.04123
$749$	−8.90108	−0.325238
$750$	−3.35701	−0.122581
$751$	4.95754	0.180903	0.0904517	−	0.995901i	$-0.471169\pi$
$751$	4.95754	0.180903	0.0904517	+	0.995901i	$0.471169\pi$
$752$	−3.58195	−0.130620
$753$	−19.1979	−0.699609
$754$	−26.1884	−0.953725
$755$	19.8464	0.722284
$756$	−34.2742	−1.24654
$757$	34.3557	1.24868	0.624339	−	0.781153i	$-0.285368\pi$
$757$	34.3557	1.24868	0.624339	+	0.781153i	$0.285368\pi$
$758$	−7.87360	−0.285982
$759$	14.5576	0.528406
$760$	6.98680	0.253438
$761$	7.08672	0.256893	0.128447	−	0.991716i	$-0.459001\pi$
$761$	7.08672	0.256893	0.128447	+	0.991716i	$0.459001\pi$
$762$	−17.0970	−0.619361
$763$	7.73400	0.279989
$764$	−8.91538	−0.322547
$765$	53.8201	1.94587
$766$	−10.7313	−0.387737
$767$	−68.2834	−2.46557
$768$	−3.35701	−0.121136
$769$	43.5556	1.57066	0.785328	−	0.619080i	$-0.212494\pi$
$769$	43.5556	1.57066	0.785328	+	0.619080i	$0.212494\pi$
$770$	8.47761	0.305512
$771$	66.9362	2.41065
$772$	15.8993	0.572229
$773$	10.3133	0.370945	0.185472	−	0.982649i	$-0.440618\pi$
$773$	10.3133	0.370945	0.185472	+	0.982649i	$0.440618\pi$
$774$	−26.1321	−0.939299
$775$	−2.57782	−0.0925980
$776$	−15.7976	−0.567101
$777$	23.0949	0.828525
$778$	28.7592	1.03107
$779$	−39.0343	−1.39855
$780$	21.2531	0.760983
$781$	1.59532	0.0570849
$782$	−6.45008	−0.230654
$783$	−73.1756	−2.61508
$784$	−3.24612	−0.115933
$785$	−4.10713	−0.146590
$786$	11.3657	0.405402
$787$	51.0762	1.82067	0.910336	−	0.413871i	$-0.135824\pi$
$787$	51.0762	1.82067	0.910336	+	0.413871i	$0.135824\pi$
$788$	25.0301	0.891661
$789$	24.8424	0.884413
$790$	−7.28525	−0.259198
$791$	18.6313	0.662451
$792$	−36.1839	−1.28574
$793$	4.95124	0.175824
$794$	2.91628	0.103495
$795$	−26.8272	−0.951464
$796$	−6.29894	−0.223260
$797$	7.53111	0.266766	0.133383	−	0.991065i	$-0.457416\pi$
$797$	7.53111	0.266766	0.133383	+	0.991065i	$0.457416\pi$
$798$	45.4435	1.60868
$799$	23.3122	0.824726
$800$	−1.00000	−0.0353553
$801$	−109.280	−3.86122
$802$	−37.0237	−1.30735
$803$	−45.9851	−1.62278
$804$	33.2622	1.17307
$805$	1.92018	0.0676776
$806$	16.3200	0.574849
$807$	−104.961	−3.69481
$808$	18.5608	0.652966
$809$	−9.60126	−0.337562	−0.168781	−	0.985654i	$-0.553983\pi$
$809$	−9.60126	−0.337562	−0.168781	+	0.985654i	$0.553983\pi$
$810$	34.5768	1.21490
$811$	−6.59126	−0.231451	−0.115725	−	0.993281i	$-0.536919\pi$
$811$	−6.59126	−0.231451	−0.115725	+	0.993281i	$0.536919\pi$
$812$	8.01457	0.281256
$813$	−82.9334	−2.90860
$814$	15.5366	0.544557
$815$	21.0807	0.738426
$816$	21.8482	0.764841
$817$	22.0786	0.772431
$818$	11.4833	0.401504
$819$	101.436	3.54445
$820$	5.58686	0.195102
$821$	−43.2819	−1.51055	−0.755275	−	0.655408i	$-0.772497\pi$
$821$	−43.2819	−1.51055	−0.755275	+	0.655408i	$0.772497\pi$
$822$	15.4443	0.538681
$823$	13.2214	0.460867	0.230434	−	0.973088i	$-0.425986\pi$
$823$	13.2214	0.460867	0.230434	+	0.973088i	$0.425986\pi$
$824$	−4.08304	−0.142239
$825$	−14.6888	−0.511398
$826$	20.8971	0.727103
$827$	−3.24008	−0.112669	−0.0563344	−	0.998412i	$-0.517941\pi$
$827$	−3.24008	−0.112669	−0.0563344	+	0.998412i	$0.517941\pi$
$828$	−8.19566	−0.284819
$829$	39.3941	1.36821	0.684106	−	0.729382i	$-0.260192\pi$
$829$	39.3941	1.36821	0.684106	+	0.729382i	$0.260192\pi$
$830$	−5.69015	−0.197508
$831$	53.1286	1.84301
$832$	6.33095	0.219486
$833$	21.1265	0.731989
$834$	−49.3752	−1.70972
$835$	8.40106	0.290731
$836$	30.5711	1.05732
$837$	45.6015	1.57622
$838$	−36.9382	−1.27601
$839$	10.3987	0.359005	0.179502	−	0.983758i	$-0.442551\pi$
$839$	10.3987	0.359005	0.179502	+	0.983758i	$0.442551\pi$
$840$	−6.50420	−0.224416
$841$	−11.8888	−0.409960
$842$	21.8683	0.753631
$843$	26.3734	0.908348
$844$	−13.2392	−0.455712
$845$	−27.0810	−0.931613
$846$	29.6211	1.01840
$847$	15.7818	0.542270
$848$	−7.99139	−0.274426
$849$	75.8399	2.60282
$850$	6.50823	0.223231
$851$	3.51905	0.120631
$852$	−1.22396	−0.0419321
$853$	27.0338	0.925620	0.462810	−	0.886458i	$-0.346841\pi$
$853$	27.0338	0.925620	0.462810	+	0.886458i	$0.346841\pi$
$854$	−1.51525	−0.0518510
$855$	−57.7777	−1.97595
$856$	4.59412	0.157024
$857$	−8.75176	−0.298954	−0.149477	−	0.988765i	$-0.547759\pi$
$857$	−8.75176	−0.298954	−0.149477	+	0.988765i	$0.547759\pi$
$858$	92.9941	3.17477
$859$	−49.8328	−1.70027	−0.850137	−	0.526562i	$-0.823481\pi$
$859$	−49.8328	−1.70027	−0.850137	+	0.526562i	$0.823481\pi$
$860$	−3.16004	−0.107756
$861$	36.3381	1.23840
$862$	−9.10953	−0.310272
$863$	−26.8440	−0.913780	−0.456890	−	0.889523i	$-0.651037\pi$
$863$	−26.8440	−0.913780	−0.456890	+	0.889523i	$0.651037\pi$
$864$	17.6900	0.601824
$865$	11.3864	0.387150
$866$	14.1771	0.481757
$867$	−85.1241	−2.89097
$868$	−4.99451	−0.169525
$869$	−31.8770	−1.08135
$870$	−13.8865	−0.470797
$871$	−62.7288	−2.12549
$872$	−3.99175	−0.135178
$873$	130.639	4.42146
$874$	6.92437	0.234220
$875$	−1.93749	−0.0654992
$876$	35.2807	1.19202
$877$	27.4426	0.926671	0.463335	−	0.886183i	$-0.346653\pi$
$877$	27.4426	0.926671	0.463335	+	0.886183i	$0.346653\pi$
$878$	−0.0571635	−0.00192918
$879$	59.5901	2.00992
$880$	−4.37555	−0.147500
$881$	45.5921	1.53604	0.768018	−	0.640428i	$-0.221243\pi$
$881$	45.5921	1.53604	0.768018	+	0.640428i	$0.221243\pi$
$882$	26.8439	0.903882
$883$	−31.1218	−1.04733	−0.523666	−	0.851924i	$-0.675436\pi$
$883$	−31.1218	−1.04733	−0.523666	+	0.851924i	$0.675436\pi$
$884$	−41.2033	−1.38582
$885$	−36.2075	−1.21710
$886$	−25.6264	−0.860936
$887$	35.8114	1.20243	0.601214	−	0.799088i	$-0.294684\pi$
$887$	35.8114	1.20243	0.601214	+	0.799088i	$0.294684\pi$
$888$	−11.9200	−0.400009
$889$	−9.86752	−0.330946
$890$	−13.2147	−0.442959
$891$	151.293	5.06849
$892$	−26.0814	−0.873270
$893$	−25.0264	−0.837476
$894$	32.7180	1.09425
$895$	4.64204	0.155166
$896$	−1.93749	−0.0647271
$897$	21.0632	0.703280
$898$	−26.2962	−0.877516
$899$	−10.6633	−0.355641
$900$	8.26955	0.275652
$901$	52.0098	1.73270
$902$	24.4456	0.813950
$903$	−20.5535	−0.683978
$904$	−9.61616	−0.319829
$905$	18.9122	0.628663
$906$	−66.6246	−2.21345
$907$	36.2636	1.20411	0.602056	−	0.798454i	$-0.294348\pi$
$907$	36.2636	1.20411	0.602056	+	0.798454i	$0.294348\pi$
$908$	−20.9408	−0.694946
$909$	−153.489	−5.09092
$910$	12.2662	0.406620
$911$	−25.9429	−0.859526	−0.429763	−	0.902942i	$-0.641403\pi$
$911$	−25.9429	−0.859526	−0.429763	+	0.902942i	$0.641403\pi$
$912$	−23.4548	−0.776666
$913$	−24.8975	−0.823989
$914$	6.37167	0.210756
$915$	2.62542	0.0867937
$916$	16.7372	0.553014
$917$	6.55970	0.216620
$918$	−115.130	−3.79987
$919$	3.15768	0.104162	0.0520811	−	0.998643i	$-0.483415\pi$
$919$	3.15768	0.104162	0.0520811	+	0.998643i	$0.483415\pi$
$920$	−0.991065	−0.0326745
$921$	−38.0834	−1.25489
$922$	−15.9140	−0.524101
$923$	2.30825	0.0759769
$924$	−28.4595	−0.936248
$925$	−3.55077	−0.116749
$926$	−1.66602	−0.0547489
$927$	33.7649	1.10899
$928$	−4.13656	−0.135789
$929$	16.8939	0.554271	0.277135	−	0.960831i	$-0.410615\pi$
$929$	16.8939	0.554271	0.277135	+	0.960831i	$0.410615\pi$
$930$	8.65378	0.283768
$931$	−22.6800	−0.743306
$932$	−12.8242	−0.420072
$933$	38.2623	1.25265
$934$	31.2528	1.02262
$935$	28.4771	0.931302
$936$	−52.3541	−1.71125
$937$	31.5652	1.03119	0.515595	−	0.856832i	$-0.327571\pi$
$937$	31.5652	1.03119	0.515595	+	0.856832i	$0.327571\pi$
$938$	19.1972	0.626812
$939$	−59.7385	−1.94949
$940$	3.58195	0.116830
$941$	19.1326	0.623704	0.311852	−	0.950131i	$-0.399051\pi$
$941$	19.1326	0.623704	0.311852	+	0.950131i	$0.399051\pi$
$942$	13.7877	0.449227
$943$	5.53695	0.180308
$944$	−10.7856	−0.351043
$945$	34.2742	1.11494
$946$	−13.8269	−0.449552
$947$	9.83309	0.319533	0.159766	−	0.987155i	$-0.448926\pi$
$947$	9.83309	0.319533	0.159766	+	0.987155i	$0.448926\pi$
$948$	24.4567	0.794317
$949$	−66.5354	−2.15983
$950$	−6.98680	−0.226682
$951$	5.52719	0.179232
$952$	12.6097	0.408681
$953$	−28.6468	−0.927960	−0.463980	−	0.885846i	$-0.653579\pi$
$953$	−28.6468	−0.927960	−0.463980	+	0.885846i	$0.653579\pi$
$954$	66.0852	2.13959
$955$	8.91538	0.288495
$956$	−5.38960	−0.174312
$957$	−60.7612	−1.96413
$958$	−12.6868	−0.409892
$959$	8.91364	0.287836
$960$	3.35701	0.108347
$961$	−24.3549	−0.785640
$962$	22.4798	0.724777
$963$	−37.9913	−1.22425
$964$	4.37644	0.140956
$965$	−15.8993	−0.511817
$966$	−6.44608	−0.207399
$967$	−1.49495	−0.0480744	−0.0240372	−	0.999711i	$-0.507652\pi$
$967$	−1.49495	−0.0480744	−0.0240372	+	0.999711i	$0.507652\pi$
$968$	−8.14548	−0.261806
$969$	152.649	4.90380
$970$	15.7976	0.507231
$971$	−31.2150	−1.00174	−0.500868	−	0.865524i	$-0.666986\pi$
$971$	−31.2150	−1.00174	−0.500868	+	0.865524i	$0.666986\pi$
$972$	−63.0049	−2.02088
$973$	−28.4968	−0.913565
$974$	−3.69894	−0.118522
$975$	−21.2531	−0.680644
$976$	0.782070	0.0250334
$977$	15.5693	0.498107	0.249054	−	0.968490i	$-0.419880\pi$
$977$	15.5693	0.498107	0.249054	+	0.968490i	$0.419880\pi$
$978$	−70.7684	−2.26292
$979$	−57.8218	−1.84799
$980$	3.24612	0.103693
$981$	33.0100	1.05393
$982$	−29.6502	−0.946176
$983$	−41.6267	−1.32768	−0.663842	−	0.747873i	$-0.731075\pi$
$983$	−41.6267	−1.32768	−0.663842	+	0.747873i	$0.731075\pi$
$984$	−18.7552	−0.597893
$985$	−25.0301	−0.797526
$986$	26.9217	0.857362
$987$	23.2977	0.741575
$988$	44.2331	1.40724
$989$	−3.13181	−0.0995856
$990$	36.1839	1.15000
$991$	−0.614249	−0.0195123	−0.00975613	−	0.999952i	$-0.503106\pi$
$991$	−0.614249	−0.0195123	−0.00975613	+	0.999952i	$0.503106\pi$
$992$	2.57782	0.0818458
$993$	31.5278	1.00051
$994$	−0.706405	−0.0224058
$995$	6.29894	0.199690
$996$	19.1019	0.605267
$997$	16.0560	0.508499	0.254249	−	0.967139i	$-0.418172\pi$
$997$	16.0560	0.508499	0.254249	+	0.967139i	$0.418172\pi$
$998$	24.9312	0.789183
$999$	62.8130	1.98731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.1	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.1	✓	29	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.35701 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.35701 q^{6} +1.93749 q^{7} -1.00000 q^{8} +8.26955 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.35701 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.35701 q^{6} +1.93749 q^{7} -1.00000 q^{8} +8.26955 q^{9} +1.00000 q^{10} +4.37555 q^{11} -3.35701 q^{12} +6.33095 q^{13} -1.93749 q^{14} +3.35701 q^{15} +1.00000 q^{16} -6.50823 q^{17} -8.26955 q^{18} +6.98680 q^{19} -1.00000 q^{20} -6.50420 q^{21} -4.37555 q^{22} -0.991065 q^{23} +3.35701 q^{24} +1.00000 q^{25} -6.33095 q^{26} -17.6900 q^{27} +1.93749 q^{28} +4.13656 q^{29} -3.35701 q^{30} -2.57782 q^{31} -1.00000 q^{32} -14.6888 q^{33} +6.50823 q^{34} -1.93749 q^{35} +8.26955 q^{36} -3.55077 q^{37} -6.98680 q^{38} -21.2531 q^{39} +1.00000 q^{40} -5.58686 q^{41} +6.50420 q^{42} +3.16004 q^{43} +4.37555 q^{44} -8.26955 q^{45} +0.991065 q^{46} -3.58195 q^{47} -3.35701 q^{48} -3.24612 q^{49} -1.00000 q^{50} +21.8482 q^{51} +6.33095 q^{52} -7.99139 q^{53} +17.6900 q^{54} -4.37555 q^{55} -1.93749 q^{56} -23.4548 q^{57} -4.13656 q^{58} -10.7856 q^{59} +3.35701 q^{60} +0.782070 q^{61} +2.57782 q^{62} +16.0222 q^{63} +1.00000 q^{64} -6.33095 q^{65} +14.6888 q^{66} -9.90828 q^{67} -6.50823 q^{68} +3.32702 q^{69} +1.93749 q^{70} +0.364597 q^{71} -8.26955 q^{72} -10.5095 q^{73} +3.55077 q^{74} -3.35701 q^{75} +6.98680 q^{76} +8.47761 q^{77} +21.2531 q^{78} -7.28525 q^{79} -1.00000 q^{80} +34.5768 q^{81} +5.58686 q^{82} -5.69015 q^{83} -6.50420 q^{84} +6.50823 q^{85} -3.16004 q^{86} -13.8865 q^{87} -4.37555 q^{88} -13.2147 q^{89} +8.26955 q^{90} +12.2662 q^{91} -0.991065 q^{92} +8.65378 q^{93} +3.58195 q^{94} -6.98680 q^{95} +3.35701 q^{96} +15.7976 q^{97} +3.24612 q^{98} +36.1839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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